The second presidential debate between Barack Obama and Mitt Romney got started just after 9 o'clock from the campus of Hofstra University in Hempstead, New York. The town-hall-style debate, with an audience of uncommitted voters selected by Gallup, was moderated by CNN's Candy Crowley.

Here are some highlights of the action:

The first question of the evening was from a college student wondering what the employment situation would be when he graduated:

Romney said keeping college costs affordable was essential, and that he had a five-point plan for the economy: "I will make sure you have a job when you graduate in 2014."

Obama answered: "Governor Romney doesn't have a five-point plan—he has a one-point plan, to make sure the people at the top play by a different set of rules."

During the next segment of the debate, the two candidates actually began speaking to each other directly (something they weren’t supposed to do) in a fairly heated exchange over American energy policy, covering oil drilling as well as gas prices. Romney at one point said, "You'll get your chance in a moment, I'm still speaking."

“It’s conceivable that Gov. Romney could bring down gas prices because with his policies, we might be back in that same mess," Obama said, referring to the economic downturn that began in 2007.

Romney on taxes: “[My policy will be] no tax on your savings. That makes life a lot easier.”

Obama: “Your first $250,000 worth of income: no change… Governor Romney’s allies in Congress have held the 98 percent hostage because they want tax breaks for the top 2 percent.”

The tax discussion continued, with things getting rather feisty again:

Romney quickly replied, "What about $5 trillion in deficits over the past four years? That's math that doesn't add up."

Obama: “Governor, you’re the last person who’s going to get tough on China.”

Romney, on what will happen next: “If you elect President Obama, you know what you’re going to get. You’re going to get a repeat of the last four years. … The middle class has been crushed under the policies of a president who doesn’t understand how to get it working again.”

The debate then turned to immigration for the first time (either this debate or the first one). Both men acknowledged America as “a nation of immigrants.”

Romney: “We’re going to have to stop illegal immigration. … I do not support amnesty."

Obama then discussed his support for the DREAM Act, and Romney’s support for Arizona’s controversial immigration law.

Things took a strange turn back to tax policy and foreign trade, with Romney reminding the president that he, too, has investments in foreign countries. Obama replied, “I don't look at my pension. It's not as big as yours."

The next subject was the assassination of several Americans, including an ambassador, in Libya last month:

Obama: “The suggest that anybody on my team – the secretary of state, the U.N. ambassador – would play politics or mislead, when we’ve lost four of our own is offensive.”

Romney accused the president of failing to publicly identify the Libyan attacks as an act of terror, at which point the moderator corrected him, saying, “He did call it an act of terror."

On outsourcing and general foreign-trade policy:

Romney: “What’s key about bringing jobs back here … is to make America the most attractive place in the world to do business,” by cutting the corporate tax rate and creating a better environment for entrepreneurs.

Obama: “There are some jobs that are not going to come back because they’re low-wage, low-skill jobs. I want high-wage, high-skill jobs.”

It was a much more high-energy debate than the last one, with multiple direct confrontations between the candidates. Obama and Romney don't seem like each other much, and they made that clear, which should probably please both of their bases.